The proposed research will develop a systematic mathematical theory linking aggregate fertility rates to individual intentions and contraceptive failure rates, as measure in surveys. It will generalize and extend the model and results of Lee, 1977a, by including the younger age groups, and by encompassing data from other developed countries and less developed countries. This should fill a conspicuous gap in demographic theory. The basic static model relate the proportion of nonterminators in a cohort to its additional desired fertility. The birth rate to nonterminators depends on desired interval length and contraceptive timing failure rates. The overall marital fertility rate depends on the birth rate to nonterminators and the contraceptive number failure rate of terminators. Dynamic analysis for a cohort follows from the observation that additional desired fertility decreases by the (wanted) marital fertility rate and increases by the rate of change of desired completed fertility. The mathematical model has numerous applications to problems of theory, policy and empirical analysis, such as accounting for the sources of the baby boom and bust, facilitating econometric analysis of fertility change over time or differences across areas, showing that turning points in marital fertility should typically precede turning points in desired completed fertility, and examining the consistency of fertility attitudes and behavior at the aggregate level.